Non-vanishing theorem for log canonical pairs

Details Non-vanishing theorem for log canonical pairs Non-vanishing theorem for log canonical pairs

2009-01-05

arxiv.org/abs/0901.0409v3

Mathematics

Algebraic Geometry

13 pages, v2: minor revisions, v3: minor revisions following referee's comments

Scientific paper

We obtain a correct generalization of Shokurov's non-vanishing theorem for
log canonical pairs. It implies the base point free theorem for log canonical
pairs. We also prove the rationality theorem for log canonical pairs. As a
corollary, we obtain the cone theorem for log canonical pairs. We do not need
Ambro's theory of quasi-log varieties.

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